• Transactions of the Korean Society of Mechanical Engineers A
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• v.41 no.3
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• pp.213-218
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• 2017

In this study, a reverse design of the F-theta lens was proposed for a 2D scanner in remote welding applications. The curvature and distance of the lens were set as variables, and the focal length of the lens was set as the marginal ray height. The ZEMAX commercial software was used to perform a simulation with unlimited iterations for the optimization process. The target value was optimized using the internal Merit function with the weight factors of focal length and spot diameter. The number of lenses was four, and the focal length obtained from the results was 135mm that is slightly less than that of the commercial lens, which is set with a focal length of 185 mm. The calculated spot diameters are $1.3{\mu}m$, $6.2{\mu}m$, and $16.1{\mu}m$ for $0^{\circ}$, $12.5^{\circ}$ and $23^{\circ}$ of incident laser beam, respectively. It is expected that an optimized lens design is possible by performing the reverse design of a lens by the ray tracing method.

• Korean Journal of Optics and Photonics
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• v.3 no.3
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• pp.161-166
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• 1992

The s-polarized laser beam is incident with an angle ~$-30^{\circ}$ to a uniformly rotating rough metal surface and the degree of second order temporal coherence $g_{s}^{(2)}(\tau)$ of the backscattered wave, which has the same polarization with the incident laser beam, is measured. The contribution of shot noise involved in the measurement of $g_{s}^{(2)}(0)$ is subtracted from the photoelectric signal to obtain the accurate value of $g_{s}^{(2)}(0)$.At each scattering angle$\theta_{s}$에서$g_{s}^{(2)}(\tau)$ is almost consistent with the function {1+exp($-\tau^2/\tau_0^2$)}, which is the same result with the case of the laser speckle formed by scattering on the rotating ground glass suface. In addition, a peak in the angular distribution of $\tau_0$ is observed with the maximum at$\theta_s=34^{\circ}$.It is found that the rough metallic scattering with multiple scattering over than 10% has the same function of the degree of second order temporal coherence with that of the ground glass surface scattering where the multiple scattering is ignorably small.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.435-450
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• 2009

On page 366 of his lost notebook [15], Ramanujan recorded a cubic continued fraction and several theorems analogous to Rogers-Ramanujan's continued fractions. In this paper, we derive several general formulas for explicit evaluations of Ramanujan's cubic continued fraction, several reciprocity theorems, two formulas connecting V (q) and V ($q^3$) and also establish some explicit evaluations using the values of remarkable product of theta-function.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.93-107
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• 1995

In their paper [2,3], Cameron and Storvick introduced some classes $S"+m$ and of functionals on classical Wiener spaces $C_0[a,b]$. For such functionals, they showed that the analytic Feynman integral exists and they gave some formulas for this integral. Moreover they obtained that the functionals of the form $$ (1.1) F(x) = exp {\int^b_a{\theta(s,x(x))dx} $$ are in S" where they assumbed that the potential $\delta : [a,b] \times R \to C$ satisfies (i) for each $s \in [a,b], \theta(s,\cdot)$ is the Fourier-Stieltjes transform of $\sigma_s \in M(R)$, (ii) for each Borel subset E of $[a,b] \times R, \sigma_s (E^{(s)})$ is a Borel measurable function of s on [a,b], and (iii) the total variation $\Vert \sigma_s \Vert$ of $\sigma_s$ is bounded as a function of s.tion of s.

• The Pure and Applied Mathematics
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• v.21 no.4
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• pp.271-279
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• 2014

Let $T_l$ be a transformation on the interval [-1, 1] defined by Chebyshev polynomial of degree $l(l{\geq}2)$, i.e., $T_l(cos{\theta})=cos(l{\theta})$. In this paper, we consider $T_l$ as a measure preserving transformation on [-1, 1] with an invariant measure $\frac{1}{\sqrt[\pi]{1-x^2}}dx$. We show that If f(x) is a nonconstant step function with finite k-discontinuity points with k < l-1, then it satisfies the Central Limit Theorem. We also give an explicit method how to check whether it satisfies the Central Limit Theorem or not in the cases of general step functions with finite discontinuity points.

• International Journal of Reliability and Applications
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• v.12 no.1
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• pp.61-77
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• 2011

One of the most important problems in the estimation of the parameter of the failure model, is the cost of experimental sampling units, which can be reduced by using any prior information available about ${\theta}$, and devising a two-stage pooling shrunken estimation procedure. We have proposed an estimator of the reliability function (R(t)) of the exponential model using two-stage time censored data when a prior value about the unknown parameter (${\theta}$) is available from the past. To compare the performance of the proposed estimator with the classical estimator, computer intensive calculations for bias, mean squared error, relative efficiency, expected sample size and percentage of the overall sample size saved expressions, were done for varying the constants involved in the proposed estimator (${\tilde{R}}$(t)).

• Journal of the Korea Safety Management & Science
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• v.4 no.3
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• pp.59-66
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• 2002

This paper presents accelerated life tests for Type I censoring data under probabilistic stresses. Probabilistic stress, S, is the random variable for stress influenced by test environments, test equipments, sampling devices and use conditions. The hazard rate, $\theta$ is a random variable of environments and a function of probabilistic stress. In detail, it is assumed that the hazard rate is linear function of the stress, the general stress distribution is a gamma distribution and the life distribution for the given hazard rate, $\theta$is an exponential distribution. Maximum likelihood estimators of model parameters are obtained, and the mean life in use stress condition is estimated. A hypothetical example is given to show its applicability.

• Bulletin of the Korean Chemical Society
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• v.21 no.12
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• pp.1227-1232
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• 2000

Near the conical intersection for the 1,2 $^{2}A'$ states of $H_3$ the derivative coupling vector is calculated and analyzed on the plane of internal coordinates, (U,V) or its polar coordinates $(S{\theta})$, based on the squares of the internuclear distances. It is shown that in the vicinity of the conical intersection the derivative coupling vector behaves like ${\theta}/2S$, which is responsible for the sign changes of the real-valued electronic wave function when the nuclear configuration traverses a closed path enclosing a conical intersection. The analytic property of the wave functions is studied and especially the observation of the sign change in the configuration state function (CSF) coefficients of the real-valued electronic wave functions is demonstrated.

• The Pure and Applied Mathematics
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• v.31 no.2
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• pp.189-200
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• 2024

We derive modular equations of degree 3 to find corresponding theta-function identities. We use them to find some new evaluations of $G(e^{-{\pi}{\sqrt{n}}})$ and $G(-e^{-{\pi}{\sqrt{n}}})$ for $n\,=\,\frac{25}{3{\cdot}4^{m-1}}$ and $\frac{4^{1-m}}{3{\cdot}25}$, where m = 0, 1, 2.

• Bulletin of the Korean Chemical Society
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• v.34 no.7
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• pp.2063-2066
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• 2013

While many eukaryotic and some prokaryotic proteins show a phosphorylation-dependent mobility shift (PDMS) on SDS-PAGE, the molecular mechanism for this phenomenon had not been elucidated. We have recently shown that the distribution of negatively charged amino acids around the phosphorylation site is important for the PDMS of some proteins. Here, we show that replacement of the phosphorylation site with a negatively charged amino acid results in a similar degree of the mobility shift of a protein as phosphorylation, indicating that the PDMS is due to the introduction of a negative charge by phosphorylation. Compared with a protein showing no shift, one showing a retarded mobility on SDS-PAGE had a decreased capacity for SDS binding. The elucidation of the consensus sequence (${\Theta}X_{1-3}{\Theta}X_{1-3}{\Theta}$, where ${\Theta}$ corresponds to an acidic function) for a PDMS suggests a general strategy for mutagenizing a phosphorylatable protein resulting in a PDMS.